Classical large deviation theorems on complete Riemannian manifolds

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2 Citations (Scopus)

Abstract

We generalize classical large deviation theorems to the setting of complete, smooth Riemannian manifolds. We prove the analogue of Mogulskii's theorem for geodesic random walks via a general approach using viscosity solutions for Hamilton–Jacobi equations. As a corollary, we also obtain the analogue of Cramér's theorem. The approach also provides a new proof of Schilder's theorem. Additionally, we provide a proof of Schilder's theorem by using an embedding into Euclidean space, together with Freidlin–Wentzell theory.

Original languageEnglish
Pages (from-to)4294-4334
Number of pages41
JournalStochastic Processes and their Applications
Volume129
Issue number11
DOIs
Publication statusPublished - 2019

Keywords

  • Cramér's theorem
  • Geodesic random walks
  • Hamilton–Jacobi equation
  • Large deviations
  • Non-linear semigroup method
  • Riemannian Brownian motion

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